I think I know your problem and you simply need to look at the notifications more closely. Not all hydral technology opportunities will be at the destroyed homeworld, something I quickly learned was that many of them would say something about the asteroid belt or something like that, and that I needed to go to one of the other planets to do a raid to get those. Those aren't against any race-owned area, just automated defenses I believe, so you don't have the reputation penalty with any races, and i believe there is an option or requirement, I don't remember which, to do the raid with the race on that planet, though I don't recall whether there was any benefit to do so instead of yourself, and I don't know what they would gain if there is that option.
